gfp2_sqrt.go

// Code generated by addchain. DO NOT EDIT.
package bn256

func (e *gfP2) expPMinus1Over4(x *gfP2) *gfP2 {
	// The sequence of 53 multiplications and 249 squarings is derived from the
	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
	//
	//	_10      = 2*1
	//	_100     = 2*_10
	//	_110     = _10 + _100
	//	_1010    = _100 + _110
	//	_1011    = 1 + _1010
	//	_1101    = _10 + _1011
	//	_10000   = _110 + _1010
	//	_10101   = _1010 + _1011
	//	_11011   = _110 + _10101
	//	_11101   = _10 + _11011
	//	_11111   = _10 + _11101
	//	_101001  = _1010 + _11111
	//	_101011  = _10 + _101001
	//	_111011  = _10000 + _101011
	//	_1000101 = _1010 + _111011
	//	_1001111 = _1010 + _1000101
	//	_1010001 = _10 + _1001111
	//	_1011011 = _1010 + _1010001
	//	_1011101 = _10 + _1011011
	//	_1011111 = _10 + _1011101
	//	_1100011 = _100 + _1011111
	//	_1101001 = _110 + _1100011
	//	_1101101 = _100 + _1101001
	//	_1101111 = _10 + _1101101
	//	_1110101 = _110 + _1101111
	//	i71      = ((_1011011 << 3 + 1) << 33 + _10101) << 8
	//	i93      = ((_11101 + i71) << 9 + _1101111) << 10 + _1110101
	//	i115     = ((2*i93 + 1) << 14 + _1110101) << 5
	//	i128     = 2*((_1101 + i115) << 9 + _1110101) + _10101
	//	i152     = ((i128 << 5 + _1011) << 9 + _111011) << 8
	//	i173     = ((_11101 + i152) << 9 + _101001) << 9 + _11111
	//	i200     = ((i173 << 8 + _101001) << 9 + _1101001) << 8
	//	i219     = ((_1100011 + i200) << 8 + _1001111) << 8 + _1011101
	//	i243     = ((i219 << 7 + _1101101) << 7 + _1011111) << 8
	//	i259     = ((_101011 + i243) << 6 + _11111) << 7 + _11011
	//	i285     = ((i259 << 9 + _1001111) << 7 + _1100011) << 8
	//	return     ((_1010001 + i285) << 8 + _1000101) << 6 + _11111
	//
	var z = new(gfP2).Set(e)
	var t0 = new(gfP2)
	var t1 = new(gfP2)
	var t2 = new(gfP2)
	var t3 = new(gfP2)
	var t4 = new(gfP2)
	var t5 = new(gfP2)
	var t6 = new(gfP2)
	var t7 = new(gfP2)
	var t8 = new(gfP2)
	var t9 = new(gfP2)
	var t10 = new(gfP2)
	var t11 = new(gfP2)
	var t12 = new(gfP2)
	var t13 = new(gfP2)
	var t14 = new(gfP2)
	var t15 = new(gfP2)
	var t16 = new(gfP2)
	var t17 = new(gfP2)
	var t18 = new(gfP2)

	t17.Square(x)
	t7.Square(t17)
	t15.Mul(t17, t7)
	t2.Mul(t7, t15)
	t13.Mul(x, t2)
	t16.Mul(t17, t13)
	t0.Mul(t15, t2)
	t14.Mul(t2, t13)
	t4.Mul(t15, t14)
	t11.Mul(t17, t4)
	z.Mul(t17, t11)
	t10.Mul(t2, z)
	t5.Mul(t17, t10)
	t12.Mul(t0, t5)
	t0.Mul(t2, t12)
	t3.Mul(t2, t0)
	t1.Mul(t17, t3)
	t18.Mul(t2, t1)
	t8.Mul(t17, t18)
	t6.Mul(t17, t8)
	t2.Mul(t7, t6)
	t9.Mul(t15, t2)
	t7.Mul(t7, t9)
	t17.Mul(t17, t7)
	t15.Mul(t15, t17)
	for s := 0; s < 3; s++ {
		t18.Square(t18)
	}
	t18.Mul(x, t18)
	for s := 0; s < 33; s++ {
		t18.Square(t18)
	}
	t18.Mul(t14, t18)
	for s := 0; s < 8; s++ {
		t18.Square(t18)
	}
	t18.Mul(t11, t18)
	for s := 0; s < 9; s++ {
		t18.Square(t18)
	}
	t17.Mul(t17, t18)
	for s := 0; s < 10; s++ {
		t17.Square(t17)
	}
	t17.Mul(t15, t17)
	t17.Square(t17)
	t17.Mul(x, t17)
	for s := 0; s < 14; s++ {
		t17.Square(t17)
	}
	t17.Mul(t15, t17)
	for s := 0; s < 5; s++ {
		t17.Square(t17)
	}
	t16.Mul(t16, t17)
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}
	t15.Mul(t15, t16)
	t15.Square(t15)
	t14.Mul(t14, t15)
	for s := 0; s < 5; s++ {
		t14.Square(t14)
	}
	t13.Mul(t13, t14)
	for s := 0; s < 9; s++ {
		t13.Square(t13)
	}
	t12.Mul(t12, t13)
	for s := 0; s < 8; s++ {
		t12.Square(t12)
	}
	t11.Mul(t11, t12)
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}
	t11.Mul(t10, t11)
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}
	t11.Mul(z, t11)
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}
	t10.Mul(t10, t11)
	for s := 0; s < 9; s++ {
		t10.Square(t10)
	}
	t9.Mul(t9, t10)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t9.Mul(t2, t9)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t9.Mul(t3, t9)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t8.Mul(t8, t9)
	for s := 0; s < 7; s++ {
		t8.Square(t8)
	}
	t7.Mul(t7, t8)
	for s := 0; s < 7; s++ {
		t7.Square(t7)
	}
	t6.Mul(t6, t7)
	for s := 0; s < 8; s++ {
		t6.Square(t6)
	}
	t5.Mul(t5, t6)
	for s := 0; s < 6; s++ {
		t5.Square(t5)
	}
	t5.Mul(z, t5)
	for s := 0; s < 7; s++ {
		t5.Square(t5)
	}
	t4.Mul(t4, t5)
	for s := 0; s < 9; s++ {
		t4.Square(t4)
	}
	t3.Mul(t3, t4)
	for s := 0; s < 7; s++ {
		t3.Square(t3)
	}
	t2.Mul(t2, t3)
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}
	t1.Mul(t1, t2)
	for s := 0; s < 8; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 6; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	return e.Set(z)
}

func (e *gfP2) expP(x *gfP2) *gfP2 {
	// The sequence of 56 multiplications and 250 squarings is derived from the
	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
	//
	//	_10      = 2*1
	//	_11      = 1 + _10
	//	_100     = 1 + _11
	//	_101     = 1 + _100
	//	_1000    = _11 + _101
	//	_1001    = 1 + _1000
	//	_1011    = _10 + _1001
	//	_1101    = _10 + _1011
	//	_10101   = _1000 + _1101
	//	_11001   = _100 + _10101
	//	_11101   = _100 + _11001
	//	_11111   = _10 + _11101
	//	_100011  = _100 + _11111
	//	_100101  = _10 + _100011
	//	_101001  = _100 + _100101
	//	_101011  = _10 + _101001
	//	_101101  = _10 + _101011
	//	_101111  = _10 + _101101
	//	_110011  = _100 + _101111
	//	_110101  = _10 + _110011
	//	_110111  = _10 + _110101
	//	_111011  = _100 + _110111
	//	_111101  = _10 + _111011
	//	_111111  = _10 + _111101
	//	_1011010 = _11101 + _111101
	//	i71      = ((_1011010 << 3 + _1001) << 33 + _10101) << 8
	//	i88      = ((_11101 + i71) << 8 + _110111) << 6 + _100011
	//	i115     = ((i88 << 6 + _101011) << 12 + _11101) << 7
	//	i128     = ((_101101 + i115) << 8 + _111111) << 2 + _11
	//	i152     = ((i128 << 5 + _1011) << 9 + _111011) << 8
	//	i173     = ((_11101 + i152) << 9 + _101001) << 9 + _11111
	//	i195     = ((i173 << 8 + _101001) << 6 + _1101) << 6
	//	i213     = ((_1011 + i195) << 7 + _1101) << 8 + _111101
	//	i234     = ((i213 << 7 + _111011) << 6 + _101101) << 6
	//	i250     = ((_101111 + i234) << 6 + _100101) << 7 + _110111
	//	i272     = ((i250 << 6 + _110011) << 6 + _11001) << 8
	//	i290     = ((_111111 + i272) << 9 + _110101) << 6 + _101
	//	return     (i290 << 9 + _101011) << 5 + _11101
	//
	var z = new(gfP2).Set(e)
	var t0 = new(gfP2)
	var t1 = new(gfP2)
	var t2 = new(gfP2)
	var t3 = new(gfP2)
	var t4 = new(gfP2)
	var t5 = new(gfP2)
	var t6 = new(gfP2)
	var t7 = new(gfP2)
	var t8 = new(gfP2)
	var t9 = new(gfP2)
	var t10 = new(gfP2)
	var t11 = new(gfP2)
	var t12 = new(gfP2)
	var t13 = new(gfP2)
	var t14 = new(gfP2)
	var t15 = new(gfP2)
	var t16 = new(gfP2)
	var t17 = new(gfP2)
	var t18 = new(gfP2)
	var t19 = new(gfP2)
	var t20 = new(gfP2)

	t3.Square(x)
	t16.Mul(x, t3)
	t10.Mul(x, t16)
	t1.Mul(x, t10)
	z.Mul(t16, t1)
	t19.Mul(x, z)
	t13.Mul(t3, t19)
	t12.Mul(t3, t13)
	t18.Mul(z, t12)
	t4.Mul(t10, t18)
	z.Mul(t10, t4)
	t15.Mul(t3, z)
	t17.Mul(t10, t15)
	t7.Mul(t3, t17)
	t14.Mul(t10, t7)
	t0.Mul(t3, t14)
	t9.Mul(t3, t0)
	t8.Mul(t3, t9)
	t5.Mul(t10, t8)
	t2.Mul(t3, t5)
	t6.Mul(t3, t2)
	t10.Mul(t10, t6)
	t11.Mul(t3, t10)
	t3.Mul(t3, t11)
	t20.Mul(z, t11)
	for s := 0; s < 3; s++ {
		t20.Square(t20)
	}
	t19.Mul(t19, t20)
	for s := 0; s < 33; s++ {
		t19.Square(t19)
	}
	t18.Mul(t18, t19)
	for s := 0; s < 8; s++ {
		t18.Square(t18)
	}
	t18.Mul(z, t18)
	for s := 0; s < 8; s++ {
		t18.Square(t18)
	}
	t18.Mul(t6, t18)
	for s := 0; s < 6; s++ {
		t18.Square(t18)
	}
	t17.Mul(t17, t18)
	for s := 0; s < 6; s++ {
		t17.Square(t17)
	}
	t17.Mul(t0, t17)
	for s := 0; s < 12; s++ {
		t17.Square(t17)
	}
	t17.Mul(z, t17)
	for s := 0; s < 7; s++ {
		t17.Square(t17)
	}
	t17.Mul(t9, t17)
	for s := 0; s < 8; s++ {
		t17.Square(t17)
	}
	t17.Mul(t3, t17)
	for s := 0; s < 2; s++ {
		t17.Square(t17)
	}
	t16.Mul(t16, t17)
	for s := 0; s < 5; s++ {
		t16.Square(t16)
	}
	t16.Mul(t13, t16)
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}
	t16.Mul(t10, t16)
	for s := 0; s < 8; s++ {
		t16.Square(t16)
	}
	t16.Mul(z, t16)
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}
	t16.Mul(t14, t16)
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}
	t15.Mul(t15, t16)
	for s := 0; s < 8; s++ {
		t15.Square(t15)
	}
	t14.Mul(t14, t15)
	for s := 0; s < 6; s++ {
		t14.Square(t14)
	}
	t14.Mul(t12, t14)
	for s := 0; s < 6; s++ {
		t14.Square(t14)
	}
	t13.Mul(t13, t14)
	for s := 0; s < 7; s++ {
		t13.Square(t13)
	}
	t12.Mul(t12, t13)
	for s := 0; s < 8; s++ {
		t12.Square(t12)
	}
	t11.Mul(t11, t12)
	for s := 0; s < 7; s++ {
		t11.Square(t11)
	}
	t10.Mul(t10, t11)
	for s := 0; s < 6; s++ {
		t10.Square(t10)
	}
	t9.Mul(t9, t10)
	for s := 0; s < 6; s++ {
		t9.Square(t9)
	}
	t8.Mul(t8, t9)
	for s := 0; s < 6; s++ {
		t8.Square(t8)
	}
	t7.Mul(t7, t8)
	for s := 0; s < 7; s++ {
		t7.Square(t7)
	}
	t6.Mul(t6, t7)
	for s := 0; s < 6; s++ {
		t6.Square(t6)
	}
	t5.Mul(t5, t6)
	for s := 0; s < 6; s++ {
		t5.Square(t5)
	}
	t4.Mul(t4, t5)
	for s := 0; s < 8; s++ {
		t4.Square(t4)
	}
	t3.Mul(t3, t4)
	for s := 0; s < 9; s++ {
		t3.Square(t3)
	}
	t2.Mul(t2, t3)
	for s := 0; s < 6; s++ {
		t2.Square(t2)
	}
	t1.Mul(t1, t2)
	for s := 0; s < 9; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 5; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	return e.Set(z)
}

func (e *gfP2) expPMinus1Over2(x *gfP2) *gfP2 {
	// The sequence of 53 multiplications and 250 squarings is derived from the
	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
	//
	//	_10      = 2*1
	//	_100     = 2*_10
	//	_110     = _10 + _100
	//	_1010    = _100 + _110
	//	_1011    = 1 + _1010
	//	_1101    = _10 + _1011
	//	_10000   = _110 + _1010
	//	_10101   = _1010 + _1011
	//	_11011   = _110 + _10101
	//	_11101   = _10 + _11011
	//	_11111   = _10 + _11101
	//	_101001  = _1010 + _11111
	//	_101011  = _10 + _101001
	//	_111011  = _10000 + _101011
	//	_1000101 = _1010 + _111011
	//	_1001111 = _1010 + _1000101
	//	_1010001 = _10 + _1001111
	//	_1011011 = _1010 + _1010001
	//	_1011101 = _10 + _1011011
	//	_1011111 = _10 + _1011101
	//	_1100011 = _100 + _1011111
	//	_1101001 = _110 + _1100011
	//	_1101101 = _100 + _1101001
	//	_1101111 = _10 + _1101101
	//	_1110101 = _110 + _1101111
	//	i71      = ((_1011011 << 3 + 1) << 33 + _10101) << 8
	//	i93      = ((_11101 + i71) << 9 + _1101111) << 10 + _1110101
	//	i115     = ((2*i93 + 1) << 14 + _1110101) << 5
	//	i128     = 2*((_1101 + i115) << 9 + _1110101) + _10101
	//	i152     = ((i128 << 5 + _1011) << 9 + _111011) << 8
	//	i173     = ((_11101 + i152) << 9 + _101001) << 9 + _11111
	//	i200     = ((i173 << 8 + _101001) << 9 + _1101001) << 8
	//	i219     = ((_1100011 + i200) << 8 + _1001111) << 8 + _1011101
	//	i243     = ((i219 << 7 + _1101101) << 7 + _1011111) << 8
	//	i259     = ((_101011 + i243) << 6 + _11111) << 7 + _11011
	//	i285     = ((i259 << 9 + _1001111) << 7 + _1100011) << 8
	//	i302     = ((_1010001 + i285) << 8 + _1000101) << 6 + _11111
	//	return     2*i302
	//
	var z = new(gfP2).Set(e)
	var t0 = new(gfP2)
	var t1 = new(gfP2)
	var t2 = new(gfP2)
	var t3 = new(gfP2)
	var t4 = new(gfP2)
	var t5 = new(gfP2)
	var t6 = new(gfP2)
	var t7 = new(gfP2)
	var t8 = new(gfP2)
	var t9 = new(gfP2)
	var t10 = new(gfP2)
	var t11 = new(gfP2)
	var t12 = new(gfP2)
	var t13 = new(gfP2)
	var t14 = new(gfP2)
	var t15 = new(gfP2)
	var t16 = new(gfP2)
	var t17 = new(gfP2)
	var t18 = new(gfP2)

	t17.Square(x)
	t7.Square(t17)
	t15.Mul(t17, t7)
	t2.Mul(t7, t15)
	t13.Mul(x, t2)
	t16.Mul(t17, t13)
	t0.Mul(t15, t2)
	t14.Mul(t2, t13)
	t4.Mul(t15, t14)
	t11.Mul(t17, t4)
	z.Mul(t17, t11)
	t10.Mul(t2, z)
	t5.Mul(t17, t10)
	t12.Mul(t0, t5)
	t0.Mul(t2, t12)
	t3.Mul(t2, t0)
	t1.Mul(t17, t3)
	t18.Mul(t2, t1)
	t8.Mul(t17, t18)
	t6.Mul(t17, t8)
	t2.Mul(t7, t6)
	t9.Mul(t15, t2)
	t7.Mul(t7, t9)
	t17.Mul(t17, t7)
	t15.Mul(t15, t17)
	for s := 0; s < 3; s++ {
		t18.Square(t18)
	}
	t18.Mul(x, t18)
	for s := 0; s < 33; s++ {
		t18.Square(t18)
	}
	t18.Mul(t14, t18)
	for s := 0; s < 8; s++ {
		t18.Square(t18)
	}
	t18.Mul(t11, t18)
	for s := 0; s < 9; s++ {
		t18.Square(t18)
	}
	t17.Mul(t17, t18)
	for s := 0; s < 10; s++ {
		t17.Square(t17)
	}
	t17.Mul(t15, t17)
	t17.Square(t17)
	t17.Mul(x, t17)
	for s := 0; s < 14; s++ {
		t17.Square(t17)
	}
	t17.Mul(t15, t17)
	for s := 0; s < 5; s++ {
		t17.Square(t17)
	}
	t16.Mul(t16, t17)
	for s := 0; s < 9; s++ {
		t16.Square(t16)
	}
	t15.Mul(t15, t16)
	t15.Square(t15)
	t14.Mul(t14, t15)
	for s := 0; s < 5; s++ {
		t14.Square(t14)
	}
	t13.Mul(t13, t14)
	for s := 0; s < 9; s++ {
		t13.Square(t13)
	}
	t12.Mul(t12, t13)
	for s := 0; s < 8; s++ {
		t12.Square(t12)
	}
	t11.Mul(t11, t12)
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}
	t11.Mul(t10, t11)
	for s := 0; s < 9; s++ {
		t11.Square(t11)
	}
	t11.Mul(z, t11)
	for s := 0; s < 8; s++ {
		t11.Square(t11)
	}
	t10.Mul(t10, t11)
	for s := 0; s < 9; s++ {
		t10.Square(t10)
	}
	t9.Mul(t9, t10)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t9.Mul(t2, t9)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t9.Mul(t3, t9)
	for s := 0; s < 8; s++ {
		t9.Square(t9)
	}
	t8.Mul(t8, t9)
	for s := 0; s < 7; s++ {
		t8.Square(t8)
	}
	t7.Mul(t7, t8)
	for s := 0; s < 7; s++ {
		t7.Square(t7)
	}
	t6.Mul(t6, t7)
	for s := 0; s < 8; s++ {
		t6.Square(t6)
	}
	t5.Mul(t5, t6)
	for s := 0; s < 6; s++ {
		t5.Square(t5)
	}
	t5.Mul(z, t5)
	for s := 0; s < 7; s++ {
		t5.Square(t5)
	}
	t4.Mul(t4, t5)
	for s := 0; s < 9; s++ {
		t4.Square(t4)
	}
	t3.Mul(t3, t4)
	for s := 0; s < 7; s++ {
		t3.Square(t3)
	}
	t2.Mul(t2, t3)
	for s := 0; s < 8; s++ {
		t2.Square(t2)
	}
	t1.Mul(t1, t2)
	for s := 0; s < 8; s++ {
		t1.Square(t1)
	}
	t0.Mul(t0, t1)
	for s := 0; s < 6; s++ {
		t0.Square(t0)
	}
	z.Mul(z, t0)
	z.Square(z)
	return e.Set(z)
}